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Mathematics 2016, 4(1), 12; doi:10.3390/math4010012

Inverse Eigenvalue Problems for Two Special Acyclic Matrices

1,†,* and 2,†
Department of Mathematics, Gurucharan College, College Road, Silchar 788004, India
Department of Mathematics, National Institute of Technology Silchar, Silchar 788010, India
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editors: Lokenath Debnath, Indranil SenGupta and Carsten Schneider
Received: 17 December 2015 / Revised: 5 February 2016 / Accepted: 26 February 2016 / Published: 3 March 2016
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In this paper, we study two inverse eigenvalue problems (IEPs) of constructing two special acyclic matrices. The first problem involves the reconstruction of matrices whose graph is a path, from given information on one eigenvector of the required matrix and one eigenvalue of each of its leading principal submatrices. The second problem involves reconstruction of matrices whose graph is a broom, the eigen data being the maximum and minimum eigenvalues of each of the leading principal submatrices of the required matrix. In order to solve the problems, we use the recurrence relations among leading principal minors and the property of simplicity of the extremal eigenvalues of acyclic matrices. View Full-Text
Keywords: inverse eigenvalue problem; leading principal minors; graph of a matrix inverse eigenvalue problem; leading principal minors; graph of a matrix

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Sharma, D.; Sen, M. Inverse Eigenvalue Problems for Two Special Acyclic Matrices. Mathematics 2016, 4, 12.

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